We discretize the domain using two-dimensional Chebyshev differentiation matrices [1]}. The boundary conditions were implemented by replacing the corresponding rows in the matrices with the discretized boundary conditions.
We prefer a temporal stability analysis since it requires less storage and computational power than what is required by the spatial stability problem. We base our results mainly on the temporal growth rate \(\omega _i\) , and utilize Gaster transformation [2]} that allows us to relate the temporal and spatial growth rates as:
\(\gamma = \omega _i/ \frac{\partial \omega _r}{\partial k}.\) 
